Is the mother sinful for the death of her child, for whom she did not know how to prepare formula, and her breast milk was not enough for him, in addition to the negligence of the father who reassured her that the child would get better?

There is no sin upon the mother if her milk is insufficient for her infant and she informs the father of that, because the responsibility of providing milk for the child or hiring a wet nurse falls upon the father. If it is established with certainty that the child's death was due to the father's negligence in providing milk, despite his ability to do so, then he must pay the expiation for accidental killing (kaffarat qatl al-khata') and the blood money (diyah) to the child's heirs. Withholding sustenance from one in dire need until death is considered accidental killing. Nevertheless, the father cannot be held liable in this case due to the impossibility of knowing the cause of death, and the default is his innocence.